Use the properties of equality to solve the equation for [tex]x[/tex].

Before applying the properties of equality, remove the parentheses from the left side:

[tex]
\begin{aligned}
20x + 27(x - 4) & = 221 \\
20x + 27 \cdot x - 27 \cdot 4 & = 221 \\
20x + 27x - 108 & = 221 \quad \text{(Simplify)}
\end{aligned}
[/tex]

Now, combine like terms on the left side of the equation:

[tex]47x - 108 = 221[/tex]

To solve the equation [tex]$ 20x + 27(x - 4) = 221 $[/tex], we can follow these steps:

1. Remove the parentheses:
- Distribute the 27 across the terms inside the parentheses:
[tex]\[
20x + 27(x - 4) = 20x + 27 \cdot x - 27 \cdot 4
\][/tex]
- Simplify:
[tex]\[
20x + 27x - 108 = 221
\][/tex]

2. Combine like terms:
- Combine the [tex]$ x $[/tex] terms on the left side:
[tex]\[
20x + 27x = 47x
\][/tex]
- This simplifies the equation to:
[tex]\[
47x - 108 = 221
\][/tex]

3. Isolate the variable ([tex]$ x $[/tex]):
- Add 108 to both sides to get rid of the constant on the left:
[tex]\[
47x - 108 + 108 = 221 + 108
\][/tex]
- Simplify:
[tex]\[
47x = 329
\][/tex]

4. Solve for [tex]$ x $[/tex]:
- Divide both sides of the equation by 47 to solve for [tex]$ x $[/tex]:
[tex]\[
x = \frac{329}{47}
\][/tex]
- This gives:
[tex]\[
x = 7
\][/tex]

So, the solution to the equation is [tex]$ x = 7 $[/tex].